Question

Find general and particular solution of dy/dx+10y=15 and y(0) = 0

Answer 1

To find the general particular solution dy/dt = 15 - 10y  

dy/(15-10y) = dt -- now integrate  

(-1/10)*ln[15 - 10y] = t + c  

ln[15 - 10y] = -10t + c  

15 - 10y = c*e^(-10t)  

10y = 15 - c*e^(-10t)  

y = 1.5 -(c/10)e^(-10t)  

If t = 0, then y = 0 = 1.5 - c/10 --> c = 15  

therefore y = 1.5[1 - e^(-10t)]  

check:  

y = 1.5[1 - e^-10t)]  

dy = 1.5[10e^(-10t)] dt = 15e^(-10t) dt  

dy/dt = 15e^(-10t)  

dy/dt + 10y = 15e^(-10t) + 15[1 - e^(-10t)]

= 15e^(-10t) + 15 - 15e^(-10t) = 1